scholarly journals Rejecting or Accepting Parameter Values in Bayesian Estimation

2018 ◽  
Vol 1 (2) ◽  
pp. 270-280 ◽  
Author(s):  
John K. Kruschke

This article explains a decision rule that uses Bayesian posterior distributions as the basis for accepting or rejecting null values of parameters. This decision rule focuses on the range of plausible values indicated by the highest density interval of the posterior distribution and the relation between this range and a region of practical equivalence (ROPE) around the null value. The article also discusses considerations for setting the limits of a ROPE and emphasizes that analogous considerations apply to setting the decision thresholds for p values and Bayes factors.

2018 ◽  
Author(s):  
John K. Kruschke

This article explains a decision rule for accepting or rejecting null values of parameters, based on Bayesian posterior distributions. The decision rule considers a range of plausible values indicated by the highest density interval (HDI) of the posterior distribution, and its relation to a region of practical equivalence (ROPE) around the null value. The article discusses considerations for setting the limits of a ROPE and emphasizes that analogous considerations apply to setting the decision thresholds for p values and Bayes factors.


1984 ◽  
Vol 7 (1) ◽  
pp. 129-150
Author(s):  
Joachim Biskup

We study operations on generalized database relations which possibly contain maybe tuples and two types of null values. The existential null value has the meaning “value at present unknown” whereas the universal null value has the meaning “value arbitrary”. For extending a usual relational operation to generalized relations we develop three requirements: adequacy, restrictedness, and feasibility. As demonstrated for the natural join as an example, we can essetially meet these requirements although we are faced with a minor tradeoff between restrictedness and feasibility.


2019 ◽  
Vol 3 (Supplement_1) ◽  
pp. S773-S773
Author(s):  
Christopher Brydges ◽  
Allison A Bielak

Abstract Objective: Non-significant p values derived from null hypothesis significance testing do not distinguish between true null effects or cases where the data are insensitive in distinguishing the hypotheses. This study aimed to investigate the prevalence of Bayesian analyses in gerontological psychology, a statistical technique that can distinguish between conclusive and inconclusive non-significant results, by using Bayes factors (BFs) to reanalyze non-significant results from published gerontological research. Method: Non-significant results mentioned in abstracts of articles published in 2017 volumes of ten top gerontological psychology journals were extracted (N = 409) and categorized based on whether Bayesian analyses were conducted. BFs were calculated from non-significant t-tests within this sample to determine how frequently the null hypothesis was strongly supported. Results: Non-significant results were directly tested with Bayes factors in 1.22% of studies. Bayesian reanalyses of 195 non-significant t-tests found that only 7.69% of the findings provided strong evidence in support of the null hypothesis. Conclusions: Bayesian analyses are rarely used in gerontological research, and a large proportion of null findings were deemed inconclusive when reanalyzed with BFs. Researchers are encouraged to use BFs to test the validity of non-significant results, and ensure that sufficient sample sizes are used so that the meaningfulness of null findings can be evaluated.


2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jaspreet Chawla ◽  
Anil Kr Ahlawat ◽  
Jyoti Gautam

Web services and agent technology play a significant role while resolving the issues related to platform interoperability. Web service interoperability organization (WS-I) provided the guidelines to remove the interoperability issues using basic profile 1.1/1.2 product. However, issues are still arising while transferring the precision values and an array with null values between different platforms like JAVA and .NET. As in a precision issue, JAVA supports data precision up to the 6th value and .NET up to the 5th value after the decimal and after increasing their limits, the whole number gets rounded off. In array with a null value issue, JAVA treats null as a value but .NET treats null as an empty string. To remove these issues, we use the WSIG-JADE framework that helps to build and demonstrate a multiagent system that does the mapping and conversions between agents and web services. It limits the number of digits to the 5th place after the decimal thereby increasing the precision in data sets, whereas it treats null as an empty string so that string length remains the same for both the platforms thereby helping in the correct count of data elements.


Author(s):  
Tamás Ferenci ◽  
Levente Kovács

Null hypothesis significance testing dominates the current biostatistical practice. However, this routine has many flaws, in particular p-values are very often misused and misinterpreted. Several solutions has been suggested to remedy this situation, the application of Bayes Factors being perhaps the most well-known. Nevertheless, even Bayes Factors are very seldom applied in medical research. This paper investigates the application of Bayes Factors in the analysis of a realistic medical problem using actual data from a representative US survey, and compares the results to those obtained with traditional means. Linear regression is used as an example as it is one of the most basic tools in biostatistics. The effect of sample size and sampling variation is investigated (with resampling) as well as the impact of the choice of prior. Results show that there is a strong relationship between p-values and Bayes Factors, especially for large samples. The application of Bayes Factors should be encouraged evenin spite of this, as the message they convey is much more instructive and scientifically correct than the current typical practice.


2021 ◽  
Vol 14 (8) ◽  
pp. 5217-5238
Author(s):  
Xin Huang ◽  
Dan Lu ◽  
Daniel M. Ricciuto ◽  
Paul J. Hanson ◽  
Andrew D. Richardson ◽  
...  

Abstract. Models are an important tool to predict Earth system dynamics. An accurate prediction of future states of ecosystems depends on not only model structures but also parameterizations. Model parameters can be constrained by data assimilation. However, applications of data assimilation to ecology are restricted by highly technical requirements such as model-dependent coding. To alleviate this technical burden, we developed a model-independent data assimilation (MIDA) module. MIDA works in three steps including data preparation, execution of data assimilation, and visualization. The first step prepares prior ranges of parameter values, a defined number of iterations, and directory paths to access files of observations and models. The execution step calibrates parameter values to best fit the observations and estimates the parameter posterior distributions. The final step automatically visualizes the calibration performance and posterior distributions. MIDA is model independent, and modelers can use MIDA for an accurate and efficient data assimilation in a simple and interactive way without modification of their original models. We applied MIDA to four types of ecological models: the data assimilation linked ecosystem carbon (DALEC) model, a surrogate-based energy exascale earth system model: the land component (ELM), nine phenological models and a stand-alone biome ecological strategy simulator (BiomeE). The applications indicate that MIDA can effectively solve data assimilation problems for different ecological models. Additionally, the easy implementation and model-independent feature of MIDA breaks the technical barrier of applications of data–model fusion in ecology. MIDA facilitates the assimilation of various observations into models for uncertainty reduction in ecological modeling and forecasting.


Sports ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 130
Author(s):  
Shaher A. I. Shalfawi ◽  
Ghazi M. K. El Kailani

Background: The purpose of the present investigation was to examine changes in strength and aerobic physical performances in young eumenorrheic female college students during the menstruation phase and different testing occasions within a menstrual cycle. Methods: A repeated measure experimental design used to investigate the variation in physical performance from different testing occasions compared to the menstruation phase. Twelve eumenorrhea female college students volunteered to participate in this study. The participants were 19.8 ± 0.8 (±SD) years old, with the body mass of 61.4 ± 11.6 kg, the height of 162.6 ± 5.1 cm, and BMI of 23.2 ± 3.8. All participants reported regular monthly menstrual cycles of 26–33 days, none of whom reported taking oral contraceptives in their entire life. None of the participants was an athlete, and their level of activity was limited to physical education classes and recreational activities. The menstrual cycles during the two cycles before testing had to be between 26 and 35 days to participate in this study. Second, there had to be no current or ongoing neuromuscular diseases or musculoskeletal injuries. Third, no one should be taking any dietary or performance-enhancing supplements that could have affected testing results during this study. The participants tested on one-repetition maximum (1RM) bench press, 1RM leg press, push-up to failure, leg press with 60% of 1RM to failure, and running 1600 m time trial. The participants were tested on four occasions based on the classical model of the menstrual cycle (i.e., 28 days; early follicular phase (menstruation phase) on day 2 (T1), late follicular phase on day 8 (T2), ovulation phase on day 14 (T3), and mid-luteal phase on day 21 (T4)). Data were analyzed using the Bayesian hierarchical model (Bayesian Estimation) with Markov Chain Monte Carlo simulation using the decision-theoretic properties of the high-density interval (HDI) + ROPE decision rule. Results: The Bayesian estimated difference from the four testing occasions neither showed that the most credible parameter values (95% HDI) were sufficiently away from the null value nor showed that the most credible parameter values are close to the null value (Rope odds ratio among all tests were spread in 12.7% < 0 < 87.3% with an effect size ranging between d = −0.01 and 0.44). Hence, no decision can be made as to whether strength and aerobic physical performances change during the menstruation phase compared to the other testing occasions within a menstrual cycle. Conclusions: It was noticed that different studies concluded different results, which make the research in menstrual cycle difficult. However, the results from this study and published studies suggest that future research should investigate and profile motivation and autonomic nervous system activity during the menstruation phase and examine the interaction effect of the three on performance compared to other testing occasions within a menstrual cycle.


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